What is the answer to log_{5}(x-3)+log_{5}(x+21)=2 ?

The answer to log_{5}(x-3)+log_{5}(x+21)=2 is x=4

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log_{5}(x-3)+log_{5}(x+21)=2

lo g_{5} (x - 3) + lo g_{5} (x + 21) = 2

x = 4

Solution steps

lo g_{5} (x - 3) + lo g_{5} (x + 21) = 2

Apply log rules

(x - 3) (x + 21) = 25

Solve

(x - 3) (x + 21) = 25 : x = 4, x = - 22

x = 4, x = - 22

Verify Solutions:

x = 4

True

, x = - 22

False

The solution is

x = 4

ln ((x + 2)^{2}) = 2

lo g_{2} (- x^{2} + 2 x) = 0

ln (x + 8) + ln (x - 8) = 0

ln (3 x + 8) = ln (2 x + 2) + ln (x - 2)

lo g_{2} (x + 2) - lo g_{2} (x - 2) = 2

What is the answer to log_{5}(x-3)+log_{5}(x+21)=2 ?
The answer to log_{5}(x-3)+log_{5}(x+21)=2 is x=4
Solve for x: log_{5}(x-3)+log_{5}(x+21)=2
The solution is x=4